I haven't seen Yesterday...but Coca-Cola and cigarettes, briefly, were both around in the 19th century, well before the Beatles were born, so the Beatles would have had very little to do with them never existing.

Coke does seem to have still been something of a novelty in England in the 1950s. For the Beatles and their British audience in the 1950s, according to Beatles biographer Mark Lewisohn, 'few things were more thrilling, more attainably American, in 1950s Britain than standing around holding a bottle of Coke.' It is worth noting here that the Beatles were a British band who were playing their version of American music, and that they were fascinated by American cultural products. Lewisohn notes a bit from a letter home from early Beatles bassist Stuart Sutcliffe where he claimed that all he drank was Coca-Cola (which Lewisohn raises an eyebrow at). John Lennon also referenced Coke in the song 'Come Together' ('he shoot Coca-Cola'), but this is about the extent to which the Beatles engaged with the brand - unlike with Michael Jackson and Pepsi in the 1980s there were no Coke advertisements featuring the Beatles.

Cigarettes, in the Beatles' world, were fairly omnipresent; Paul McCartney's grandfather Joe worked for Cope Cigarettes all his life. John Lennon's father Alf spent a month in prison in Algeria, charged with attempting to sell some of his ship's cargo (including cigarettes) on the black market. The young Ringo, back when he was Richy, started smoking at age 11. All of the Beatles smoked cigarettes by the time John, Paul and George were playing music together. Famously, more recent editions of the Beatles record Abbey Road feature an edited version of the original cover, edited to remove the cigarette between the fingers of Paul McCartney as he crossed the road. Nonetheless I don't see any reason why the Beatles' popularity would have anything to do with the popularity of the word 'cigarette'. So these are likely choices made by the filmmakers, perhaps to illustrate the 'butterfly effect' inherent in alternate universes - one small change (cigarettes being called something else) can have big effects (like the non-existence of the Beatles, perhaps).